Lexicographic Ordering

Do you understand how a dictionary is ordered?
The word “abet” comes before “about” why.
That is Lexicographic Ordering.

If we have lexicographic ordering on $\mathbb{N} \times \mathbb{N} \times \mathbb{N}$ here are some examples.
$\begin{gathered}<br /> \left( {1,3,2} \right) \prec \left( {2,1,1} \right)\text{ because } 1 < 2. \hfill \\<br /> \left( {2,1,2} \right) \prec \left( {2,2,1} \right) \text{ because }2 = 2 \wedge 1 < 2. \hfill \\<br /> \left( {3,3,2} \right) \prec \left( {3,3,3} \right) \text{ because }3 = 3 \wedge 3 = 3 \wedge 2 < 3. \hfill \\ \end{gathered}$

I hope this give some guidance that helps you.